What is the Greatest Common Factor of 27216 and 27234?

Greatest common factor (GCF) of 27216 and 27234 is 18.

GCF(27216,27234) = 18

We will now calculate the prime factors of 27216 and 27234, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27216 and 27234.

How to find the GCF of 27216 and 27234?

We will first find the prime factorization of 27216 and 27234. After we will calculate the factors of 27216 and 27234 and find the biggest common factor number .

Step-1: Prime Factorization of 27216

Prime factors of 27216 are 2, 3, 7. Prime factorization of 27216 in exponential form is:

27216 = 2⁴ × 3⁵ × 7¹

Step-2: Prime Factorization of 27234

Prime factors of 27234 are 2, 3, 17, 89. Prime factorization of 27234 in exponential form is:

27234 = 2¹ × 3² × 17¹ × 89¹

Step-3: Factors of 27216

List of positive integer factors of 27216 that divides 27216 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 27, 28, 36, 42, 48, 54, 56, 63, 72, 81, 84, 108, 112, 126, 144, 162, 168, 189, 216, 243, 252, 324, 336, 378, 432, 486, 504, 567, 648, 756, 972, 1008, 1134, 1296, 1512, 1701, 1944, 2268, 3024, 3402, 3888, 4536, 6804, 9072, 13608

Step-4: Factors of 27234

List of positive integer factors of 27234 that divides 27216 without a remainder.

1, 2, 3, 6, 9, 17, 18, 34, 51, 89, 102, 153, 178, 267, 306, 534, 801, 1513, 1602, 3026, 4539, 9078, 13617

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27216 and 27234. The biggest common factor number is the GCF number.
So the greatest common factor 27216 and 27234 is 18.

Also check out the Least Common Multiple of 27216 and 27234